Dynamic Graph Drawing Research Articles

Event‐based Dynamic Graph Drawing without the Agonizing Pain

AbstractTemporal networks can naturally model real‐world complex phenomena such as contact networks, information dissemination and physical proximity. However, nodes and edges bear real‐time coordinates, making it difficult to organize them into discrete timeslices, without a loss of temporal information due to projection. Event‐based dynamic graph drawing rejects the notion of a timeslice and allows each node and edge to retain its own real‐valued time coordinate. While existing work has demonstrated clear advantages for this approach, they come at a running time cost. We investigate the problem of accelerating event‐based layout to make it more competitive with existing layout techniques. In this paper, we describe the design, implementation and experimental evaluation of MultiDynNoS, the first multi‐level event‐based graph layout algorithm. We consider three operators for coarsening and placement, inspired by Walshaw, GRIP and FM3, which we couple with an event‐based graph drawing algorithm. We also propose two extensions to the core algorithm: AutoTau and Bend Transfer. We perform two experiments: first, we compare MultiDynNoS variants to existing state‐of‐the‐art dynamic graph layout approaches; second, we investigate the impact of each of the proposed algorithm extensions. MultiDynNoS proves to be competitive with existing approaches, and the proposed extensions achieve their design goals and contribute in opening new research directions.

Visualizing Uncertainty in Probabilistic Graphs with Network Hypothetical Outcome Plots (NetHOPs).

Probabilistic graphs are challenging to visualize using the traditional node-link diagram. Encoding edge probability using visual variables like width or fuzziness makes it difficult for users of static network visualizations to estimate network statistics like densities, isolates, path lengths, or clustering under uncertainty. We introduce Network Hypothetical Outcome Plots (NetHOPs), a visualization technique that animates a sequence of network realizations sampled from a network distribution defined by probabilistic edges. NetHOPs employ an aggregation and anchoring algorithm used in dynamic and longitudinal graph drawing to parameterize layout stability for uncertainty estimation. We present a community matching algorithm to enable visualizing the uncertainty of cluster membership and community occurrence. We describe the results of a study in which 51 network experts used NetHOPs to complete a set of common visual analysis tasks and reported how they perceived network structures and properties subject to uncertainty. Participants' estimates fell, on average, within 11% of the ground truth statistics, suggesting NetHOPs can be a reasonable approach for enabling network analysts to reason about multiple properties under uncertainty. Participants appeared to articulate the distribution of network statistics slightly more accurately when they could manipulate the layout anchoring and the animation speed. Based on these findings, we synthesize design recommendations for developing and using animated visualizations for probabilistic networks.

Event-Based Dynamic Graph Visualisation.

Dynamic graph drawing algorithms take as input a series of timeslices that standard, force-directed algorithms can exploit to compute a layout. However, often dynamic graphs are expressed as a series of events where the nodes and edges have real coordinates along the time dimension that are not confined to discrete timeslices. Current techniques for dynamic graph drawing impose a set of timeslices on this event-based data in order to draw the dynamic graph, but it is unclear how many timeslices should be selected: too many timeslices slows the computation of the layout, while too few timeslices obscures important temporal features, such as causality. To address these limitations, we introduce a novel model for drawing event-based dynamic graphs and the first dynamic graph drawing algorithm, DynNoSlice, that is capable of drawing dynamic graphs in this model. DynNoSlice is an offline, force-directed algorithm that draws event-based, dynamic graphs in the space-time cube (2D+time). We also present a method to extract representative small multiples from the space-time cube. To demonstrate the advantages of our approach, DynNoSlice is compared with state-of-the-art timeslicing methods using a metrics-based experiment. Finally, we present case studies of event-based dynamic data visualised with the new model and algorithm.

Tabu search for the dynamic Bipartite Drawing Problem

Drawings of graphs have many applications and they are nowadays well-established tools in computer science in general, and optimization in particular. Project scheduling is one of the many areas in which representation of graphs constitutes an important instrument. The experience shows that the main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion to achieve it. Incremental or dynamic graph drawing is an emerging topic in this context, where we seek to preserve the layout of a graph over successive drawings. In this paper, we target the edge crossing reduction in the context of incremental graph drawing. Specifically, we apply a mathematical programming formulation and several heuristic methods based on the tabu search methodology to solve it. In line with the previous paper on this topic, we consider bipartite graphs in our experimentation. The extensive computational experiments with more than 1000 instances show the superiority of our proposals in both, quality and computing time.

The “Map” in the mental map: Experimental results in dynamic graph drawing

Preserving the mental map is frequently cited by dynamic graph drawing algorithm designers as an important optimization criterion. There have been a number of definitions for mental map preservation and many different algorithmic approaches to drive dynamic graph drawing to satisfy these definitions. One of the most frequently used definitions is that of Coleman and Parker where “the placement of existing nodes and edges should change as little as possible when a change is made to the graph.” A number of experiments have been run to test the effectiveness of this definition from a usability perspective. To date, no experiment has found conclusive evidence that supports the effectiveness of the mental map in the comprehension of a dynamic graph series. In this paper, we summarize the experiments conducted on this definition of mental map preservation and provide recommendations to designers and researchers to fully understand when the mental map supports user tasks.

From encounters to plausible mobility

Inferring plausible node mobility based only on information from wireless contact traces is a difficult problem. Working with mobility information allows richer protocol simulations, particularly in dense networks, but requires complex set-ups to measure. On the other hand, contact information is easier to measure but only allows for simplistic simulation models. In a contact trace a lot of node movement information is irretrievably lost so the original positions and velocities are in general out of reach. In this paper, we propose a fast heuristic algorithm, inspired by dynamic force-based graph drawing, capable of inferring a plausible movement from any contact trace, and evaluate it on both synthetic and real-life contact traces. Our results reveal that (i) the quality of the inferred mobility is directly linked to the precision of the measured contact trace, and (ii) the simple addition of appropriate anticipation forces between nodes leads to an accurate inferred mobility.

Visualization of the High Level Structure of the Internet with Hermes

Hermes is a system for exploring and visualizing the Internet structure at the level of the Autonomous Systems and their interconnections. It relies on a three-tier architecture, on a large repository of routing information coming from heterogeneous sources, and on sophisticated graph drawing engine. Such an engine exploits static and dynamic graph drawing techniques, specifically devised for the visualization of large graphs with high density.

Fully Dynamic 3-Dimensional Orthogonal Graph Drawing

In a 3-dimensional orthogonal drawing of a graph, vertices are mapped to grid points on an integer lattice and edges are routed along integer grid lines. In this paper, we present a layout scheme that draws any graph with n vertices of maximum degree 6, using at most 6 bends per edge and in a volume of O(n2). The advantage of our strategy over other drawing methods is that our method is fully dynamic, allowing both insertion and deletion of vertices and edges, while maintaining the volume and bend bounds. The drawing can be obtained in O(n) time and insertions/deletions can be performed in O(1) time. Multiple edges and self loops are permitted. A more elaborate construction that uses only 5 bends per edge, and a simpler, more balanced layout that requires at most 7 bends per edge are also described.

A force-directed algorithm that preserves edge-crossing properties

We present an iterative drawing algorithm for undirected graphs, based on a force-directed approach, that preserves edge-crossing properties. This algorithm ensures that two edges cross in the final drawing if and only if these edges crossed in the initial layout. Therefore no new edge crossings are introduced. We describe applications of this technique to improve classical algorithms for drawing planar graphs and for dynamic graph drawing.

Dynamic graph drawing (abstract)

An automatic layout facility is a tool that receives as input a graph-like structure and is able to produce a diagram that nicely represents such a structure. Because of the increasing number of systems that manage diagrams, automatic layout facilities and algorithms for graphs layout have been extensively studied in the last years. We present a new approach in designing an automatic layout facility. Our approach is based on a modular management of a collection of algorithms and on a tool that is able to automatically select the best algorithm for a given application. Such approach has been used for devising the automatic layout facility of Diagram Server, a network server that offers to its clients several facilities for managing diagrams. (Joint work with P. Bertolazzi and G. Di Battista.)